A Hamiltonian-Free Description of Single Particle Dynamics for Hopelessly Complex Periodic Systems

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We develop a picture of periodic systems which does not rely on the Hamiltonian of the system but on maps between a finite number of time locations. Moser or Deprit-like normalizations are done directly on the maps thereby avoiding the complex time-dependent theory. We redefine linear and nonlinear Floquet variables entirely in terms of maps. This approach relies heavily on the Lie representation of maps introduced by Dragt and Finn. One might say that although we do not use the Hamiltonian in the normalization transformation, we are using Lie operators which are themselves, in some sense, pseudo-Hamiltonians for the maps … continued below

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Forest, E. January 1, 1990.

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We develop a picture of periodic systems which does not rely on the Hamiltonian of the system but on maps between a finite number of time locations. Moser or Deprit-like normalizations are done directly on the maps thereby avoiding the complex time-dependent theory. We redefine linear and nonlinear Floquet variables entirely in terms of maps. This approach relies heavily on the Lie representation of maps introduced by Dragt and Finn. One might say that although we do not use the Hamiltonian in the normalization transformation, we are using Lie operators which are themselves, in some sense, pseudo-Hamiltonians for the maps they represent. Our techniques find application in accelerator dynamics or in any field where the Hamiltonian is periodic but hopelessly complex, such as magnetic field design in stellarators.

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  • Journal Name: Journal of mathematical physics; Journal Volume: 31; Journal Issue: 5; Related Information: Journal Publication Date: 1990

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  • Report No.: LBL-28471
  • Grant Number: DE-AC02-05CH11231
  • Office of Scientific & Technical Information Report Number: 1000482
  • Archival Resource Key: ark:/67531/metadc836068

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  • January 1, 1990

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  • May 19, 2016, 3:16 p.m.

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Forest, E. A Hamiltonian-Free Description of Single Particle Dynamics for Hopelessly Complex Periodic Systems, article, January 1, 1990; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc836068/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.

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